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Kristen M, Voss JN, Wildermuth M, Bilmes A, Lisenfeld J, Rotzinger H, Ustinov AV. Giant Two-Level Systems in a Granular Superconductor. PHYSICAL REVIEW LETTERS 2024; 132:217002. [PMID: 38856245 DOI: 10.1103/physrevlett.132.217002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Revised: 02/09/2024] [Accepted: 02/11/2024] [Indexed: 06/11/2024]
Abstract
Disordered thin films are a common choice of material for superconducting, high impedance circuits used in quantum information or particle detector physics. A wide selection of materials with different levels of granularity are available, but, despite low microwave losses being reported for some, the high degree of disorder always implies the presence of intrinsic defects. Prominently, quantum circuits are prone to interact with two-level systems (TLS), typically originating from solid state defects in the dielectric parts of the circuit, like surface oxides or tunneling barriers. We present an experimental investigation of TLS in granular aluminum thin films under applied mechanical strain and electric fields. The analysis reveals a class of strongly coupled TLS having electric dipole moments up to 30 eÅ, an order of magnitude larger than dipole moments commonly reported for solid state defects. Notably, these large dipole moments appear more often in films with a higher resistivity. Our observations shed new light on granular superconductors and may have implications for their usage as a quantum circuit material.
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Affiliation(s)
- M Kristen
- Institute for Quantum Materials and Technology, Karlsruher Institute of Technology, 76131 Karlsruhe, Germany
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - J N Voss
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - M Wildermuth
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - A Bilmes
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - J Lisenfeld
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - H Rotzinger
- Institute for Quantum Materials and Technology, Karlsruher Institute of Technology, 76131 Karlsruhe, Germany
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - A V Ustinov
- Institute for Quantum Materials and Technology, Karlsruher Institute of Technology, 76131 Karlsruhe, Germany
- Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
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2
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Cheng R, Goteti US, Walker H, Krause KM, Oeding L, Hamilton MC. Toward Learning in Neuromorphic Circuits Based on Quantum Phase Slip Junctions. Front Neurosci 2021; 15:765883. [PMID: 34819835 PMCID: PMC8606638 DOI: 10.3389/fnins.2021.765883] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 10/11/2021] [Indexed: 11/13/2022] Open
Abstract
We explore the use of superconducting quantum phase slip junctions (QPSJs), an electromagnetic dual to Josephson Junctions (JJs), in neuromorphic circuits. These small circuits could serve as the building blocks of neuromorphic circuits for machine learning applications because they exhibit desirable properties such as inherent ultra-low energy per operation, high speed, dense integration, negligible loss, and natural spiking responses. In addition, they have a relatively straight-forward micro/nano fabrication, which shows promise for implementation of an enormous number of lossless interconnections that are required to realize complex neuromorphic systems. We simulate QPSJ-only, as well as hybrid QPSJ + JJ circuits for application in neuromorphic circuits including artificial synapses and neurons, as well as fan-in and fan-out circuits. We also design and simulate learning circuits, where a simplified spike timing dependent plasticity rule is realized to provide potential learning mechanisms. We also take an alternative approach, which shows potential to overcome some of the expected challenges of QPSJ-based neuromorphic circuits, via QPSJ-based charge islands coupled together to generate non-linear charge dynamics that result in a large number of programmable weights or non-volatile memory states. Notably, we show that these weights are a function of the timing and frequency of the input spiking signals and can be programmed using a small number of DC voltage bias signals, therefore exhibiting spike-timing and rate dependent plasticity, which are mechanisms to realize learning in neuromorphic circuits.
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Affiliation(s)
- Ran Cheng
- Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, United States.,Alabama Micro/Nano Science and Technology Center, Auburn University, Auburn, AL, United States
| | - Uday S Goteti
- Department of Physics, University of California, San Diego, San Diego, CA, United States
| | - Harrison Walker
- Alabama Micro/Nano Science and Technology Center, Auburn University, Auburn, AL, United States.,Department of Materials Engineering, Auburn University, Auburn, AL, United States
| | - Keith M Krause
- Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, United States.,Alabama Micro/Nano Science and Technology Center, Auburn University, Auburn, AL, United States
| | - Luke Oeding
- Department of Mathematics and Statistics, Auburn University, Auburn, AL, United States
| | - Michael C Hamilton
- Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, United States.,Alabama Micro/Nano Science and Technology Center, Auburn University, Auburn, AL, United States
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3
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Voss JN, Schön Y, Wildermuth M, Dorer D, Cole JH, Rotzinger H, Ustinov AV. Eliminating Quantum Phase Slips in Superconducting Nanowires. ACS NANO 2021; 15:4108-4114. [PMID: 33596045 DOI: 10.1021/acsnano.0c08721] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In systems with reduced dimensions, quantum fluctuations have a strong influence on the electronic conduction, even at very low temperatures. In superconductors, this is especially interesting, since the coherent state of the superconducting electrons strongly interacts with these fluctuations and therefore is a sensitive tool to study them. In this paper, we report on comprehensive measurements of superconducting nanowires in the quantum phase slip regime. Using an intrinsic electromigration process, we have developed a method to lower the nanowire's resistance in situ and therefore eliminate quantum phase slips in small consecutive steps. We observe critical (Coulomb) blockade voltages and superconducting critical currents, in good agreement with theoretical models. Between these two regimes, we find a continuous transition displaying a nonlinear metallic-like behavior. The reported intrinsic electromigration technique is not limited to low temperatures, as we find a similar change in resistance that spans over 3 orders of magnitude also at room temperature. Aside from superconducting quantum circuits, such a technique to reduce the resistance may also have applications in modern electronic circuits.
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Affiliation(s)
- Jan Nicolas Voss
- Physikalisches Institut, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
| | - Yannick Schön
- Physikalisches Institut, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
| | - Micha Wildermuth
- Physikalisches Institut, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
| | - Dominik Dorer
- Physikalisches Institut, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
| | - Jared H Cole
- Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, Victoria 3000, Australia
| | - Hannes Rotzinger
- Physikalisches Institut, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
- Institute for Quantum Materials and Technologies, Karlsruher Institut für Technologie, 76021 Karlsruhe, Germany
| | - Alexey V Ustinov
- Physikalisches Institut, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
- Institute for Quantum Materials and Technologies, Karlsruher Institut für Technologie, 76021 Karlsruhe, Germany
- National University of Science and Technology MISIS, Moscow 119049, Russia
- Russian Quantum Center, Skolkovo, Moscow 143025, Russia
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4
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Arutyunov KY, Lehtinen JS. High dynamic resistance elements based on a Josephson junction array. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2020; 11:417-420. [PMID: 32215228 PMCID: PMC7082698 DOI: 10.3762/bjnano.11.32] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 02/18/2020] [Indexed: 06/10/2023]
Abstract
A chain of superconductor-insulator-superconductor junctions based on Al-AlO x -Al nanostructures and fabricated using conventional lift-off lithography techniques was measured at ultra-low temperatures. At zero magnetic field, the low current bias dynamic resistance can reach values of ≈1011 Ω. It was demonstrated that the system can provide a decent quality current biasing circuit, enabling the observation of Coulomb blockade and Bloch oscillations in ultra-narrow Ti nanowires associated with the quantum phase-slip effect.
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Affiliation(s)
- Konstantin Yu Arutyunov
- National Research University Higher School of Economics, 101000, Moscow, Russia
- P.L. Kapitza Institute for Physical Problems RAS, Moscow, 119334, Russia
| | - Janne Samuel Lehtinen
- VTT Technical Research Centre of Finland Ltd., 02150 Espoo, Finland
- Department of Physics, University of Jyvaskyla, PB 35, FI-40014 Jyvaskyla, Finland
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5
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Constantino NGN, Anwar MS, Kennedy OW, Dang M, Warburton PA, Fenton JC. Emergence of Quantum Phase-Slip Behaviour in Superconducting NbN Nanowires: DC Electrical Transport and Fabrication Technologies. NANOMATERIALS 2018; 8:nano8060442. [PMID: 29914174 PMCID: PMC6027443 DOI: 10.3390/nano8060442] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/15/2018] [Revised: 06/11/2018] [Accepted: 06/13/2018] [Indexed: 12/03/2022]
Abstract
Superconducting nanowires undergoing quantum phase-slips have potential for impact in electronic devices, with a high-accuracy quantum current standard among a possible toolbox of novel components. A key element of developing such technologies is to understand the requirements for, and control the production of, superconducting nanowires that undergo coherent quantum phase-slips. We present three fabrication technologies, based on using electron-beam lithography or neon focussed ion-beam lithography, for defining narrow superconducting nanowires, and have used these to create nanowires in niobium nitride with widths in the range of 20–250 nm. We present characterisation of the nanowires using DC electrical transport at temperatures down to 300 mK. We demonstrate that a range of different behaviours may be obtained in different nanowires, including bulk-like superconducting properties with critical-current features, the observation of phase-slip centres and the observation of zero conductance below a critical voltage, characteristic of coherent quantum phase-slips. We observe critical voltages up to 5 mV, an order of magnitude larger than other reports to date. The different prominence of quantum phase-slip effects in the various nanowires may be understood as arising from the differing importance of quantum fluctuations. Control of the nanowire properties will pave the way for routine fabrication of coherent quantum phase-slip nanowire devices for technology applications.
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Affiliation(s)
- Nicolas G N Constantino
- London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UK.
| | - Muhammad Shahbaz Anwar
- London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UK.
| | - Oscar W Kennedy
- London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UK.
| | - Manyu Dang
- London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UK.
| | - Paul A Warburton
- London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UK.
| | - Jonathan C Fenton
- London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UK.
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6
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Arutyunov KY, Lehtinen JS. Quantum Fluctuations of a Superconductor Order Parameter. NANOSCALE RESEARCH LETTERS 2016; 11:364. [PMID: 27535694 PMCID: PMC4988958 DOI: 10.1186/s11671-016-1582-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/26/2016] [Accepted: 08/12/2016] [Indexed: 06/06/2023]
Abstract
Tunneling I-V characteristics between very narrow titanium nanowires and "massive" superconducting aluminum were measured. The clear trend was observed: the thinner the titanium electrode, the broader the singularity at eV = Δ1(Al) + Δ2(Ti). The phenomenon can be explained by broadening of the gap edge of the quasi-one-dimensional titanium channels due to quantum fluctuations of the order parameter modulus |Δ2|. The range of the nanowire diameters, where the effect is pronounced, correlates with dimensions where the phase fluctuations of the complex superconducting order parameter Δ = |Δ|e(iφ), the quantum phase slips, broadening the R(T) dependencies, have been observed.
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Affiliation(s)
- K. Yu Arutyunov
- National Research University Higher School of Economics, Moscow Institute of Electronics and Mathematics 101000, Moscow, Russia
| | - J. S. Lehtinen
- VTT Technical Research Centre of Finland Ltd., Centre for Metrology MIKES, P.O. Box 1000, Espoo, FI-02044 VTT Finland
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7
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Bell MT, Zhang W, Ioffe LB, Gershenson ME. Spectroscopic Evidence of the Aharonov-Casher Effect in a Cooper Pair Box. PHYSICAL REVIEW LETTERS 2016; 116:107002. [PMID: 27015505 DOI: 10.1103/physrevlett.116.107002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2015] [Indexed: 06/05/2023]
Abstract
We observe the effect of the Aharonov-Casher (AC) interference on the spectrum of a superconducting system containing a symmetric Cooper pair box (CPB) and a large inductance. By varying the charge n_{g} induced on the CPB island, we observe oscillations of the device spectrum with the period Δn_{g}=2e. These oscillations are attributed to the charge-controlled AC interference between the fluxon tunneling processes in the CPB Josephson junctions. The measured phase and charge dependences of the frequencies of the |0⟩→|1⟩ and |0⟩→|2⟩ transitions are in good agreement with our numerical simulations. Almost complete suppression of the single fluxon tunneling due to destructive interference is observed for the charge n_{g}=e(2n+1). The CPB in this regime enables fluxon pairing, which can be used for the development of parity-protected superconducting qubits.
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Affiliation(s)
- M T Bell
- Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
- Department of Electrical Engineering, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - W Zhang
- Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
| | - L B Ioffe
- Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
- LPTHE, CNRS UMR 7589, 4 place Jussieu, 75252 Paris, France
| | - M E Gershenson
- Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
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Cirillo C, Prischepa SL, Trezza M, Bondarenko VP, Attanasio C. Superconducting nanowire quantum interference device based on Nb ultrathin films deposited on self-assembled porous Si templates. NANOTECHNOLOGY 2014; 25:425205. [PMID: 25277511 DOI: 10.1088/0957-4484/25/42/425205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Magnetoresistance oscillations were observed on networks of superconducting ultrathin Nb nanowires presenting evidence of either thermal or quantum activated phase slips. The magnetic transport data, discussed in the framework of different scenarios, reveal that the system behaves coherently in the temperature range where the contribution of the fluctuations is important.
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Affiliation(s)
- C Cirillo
- CNR-SPIN Salerno and Dipartimento di Fisica 'E.R. Caianiello', Università degli Studi di Salerno, via Giovanni Paolo II, Fisciano (SA) I-84084, Italy
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9
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Lotkhov SV. Ultra-high-ohmic microstripline resistors for Coulomb blockade devices. NANOTECHNOLOGY 2013; 24:235201. [PMID: 23670293 DOI: 10.1088/0957-4484/24/23/235201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
In this paper, we report on the fabrication and low-temperature characterization of ultra-high-ohmic microstripline resistors made of a thin film of weakly oxidized titanium. Nearly linear voltage-current characteristics were measured at temperatures down to T ~ 20 mK for films with sheet resistivities as high as ~7 kΩ, i.e. about an order of magnitude higher than our previous findings for weakly oxidized Cr. Our analysis indicates that such an improvement can help to create an advantageous high-impedance environment for different Coulomb blockade devices. Further properties of the Ti film addressed in this work show the promise of low-noise behavior of the resistors when applied in different realizations of the quantum standard of current.
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Affiliation(s)
- Sergey V Lotkhov
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany.
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10
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Hriscu AM, Nazarov YV. Quantum synchronization of conjugated variables in a superconducting device leads to the fundamental resistance quantization. PHYSICAL REVIEW LETTERS 2013; 110:097002. [PMID: 23496738 DOI: 10.1103/physrevlett.110.097002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2012] [Indexed: 06/01/2023]
Abstract
We propose a way to achieve quantum synchronization of two canonically conjugated variables. For this, we employ a superconducting device where the synchronization of Josephson and Bloch oscillations results in the quantization of transresistance similar to that in the (fractional) quantum Hall effect. An LC oscillator is a key component to achieve an exponentially small rate of synchronization errors.
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Affiliation(s)
- A M Hriscu
- Kavli Institute of Nanoscience, Delft University of Technology, P. O. Box 5046, 2600 GA Delft, The Netherlands
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11
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Lehtinen JS, Zakharov K, Arutyunov KY. Coulomb blockade and BLOCH oscillations in superconducting Ti nanowires. PHYSICAL REVIEW LETTERS 2012; 109:187001. [PMID: 23215316 DOI: 10.1103/physrevlett.109.187001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2012] [Indexed: 06/01/2023]
Abstract
Quantum fluctuations in quasi-one-dimensional superconducting channels leading to spontaneous changes of the phase of the order parameter by 2π, alternatively called quantum phase slips (QPS), manifest themselves as the finite resistance well below the critical temperature of thin superconducting nanowires and the suppression of persistent currents in tiny superconducting nanorings. Here we report the experimental evidence that in a current-biased superconducting nanowire the same QPS process is responsible for the insulating state--the Coulomb blockade. When exposed to rf radiation, the internal Bloch oscillations can be synchronized with the external rf drive leading to formation of quantized current steps on the I-V characteristic. The effects originate from the fundamental quantum duality of a Josephson junction and a superconducting nanowire governed by QPS--the QPS junction.
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Affiliation(s)
- J S Lehtinen
- Department of Physics, University of Jyväskylä, PB 35, 40014 Jyväskylä, Finland
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12
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Astafiev OV, Ioffe LB, Kafanov S, Pashkin YA, Arutyunov KY, Shahar D, Cohen O, Tsai JS. Coherent quantum phase slip. Nature 2012; 484:355-8. [PMID: 22517162 DOI: 10.1038/nature10930] [Citation(s) in RCA: 193] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2011] [Accepted: 02/03/2012] [Indexed: 11/09/2022]
Abstract
A hundred years after the discovery of superconductivity, one fundamental prediction of the theory, coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual to the Josephson effect; whereas the latter is a coherent transfer of charges between superconducting leads, the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations of incoherent phase slip, CQPS has been only a subject of theoretical study. Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors near the superconductor-insulator transition. Here we report direct observation of CQPS in a narrow segment of a superconducting loop made of strongly disordered indium oxide; the effect is made manifest through the superposition of quantum states with different numbers of flux quanta. As with the Josephson effect, our observation should lead to new applications in superconducting electronics and quantum metrology.
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Affiliation(s)
- O V Astafiev
- NEC Green Innovation Research Laboratories, 34 Miyukigaoka, Tsukuba, Ibaraki, 305-8501, Japan.
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13
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Arutyunov KY, Hongisto TT, Lehtinen JS, Leino LI, Vasiliev AL. Quantum phase slip phenomenon in ultra-narrow superconducting nanorings. Sci Rep 2012; 2:293. [PMID: 22389762 PMCID: PMC3290819 DOI: 10.1038/srep00293] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2012] [Accepted: 02/13/2012] [Indexed: 11/09/2022] Open
Abstract
The smaller the system, typically - the higher is the impact of fluctuations. In narrow superconducting wires sufficiently close to the critical temperature T(c) thermal fluctuations are responsible for the experimentally observable finite resistance. Quite recently it became possible to fabricate sub-10 nm superconducting structures, where the finite resistivity was reported within the whole range of experimentally obtainable temperatures. The observation has been associated with quantum fluctuations capable to quench zero resistivity in superconducting nanowires even at temperatures T→0. Here we demonstrate that in tiny superconducting nanorings the same phenomenon is responsible for suppression of another basic attribute of superconductivity - persistent currents - dramatically affecting their magnitude, the period and the shape of the current-phase relation. The effect is of fundamental importance demonstrating the impact of quantum fluctuations on the ground state of a macroscopically coherent system, and should be taken into consideration in various nanoelectronic applications.
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Affiliation(s)
- Konstantin Yu. Arutyunov
- NanoScience Center, Department of Physics, University of Jyväskylä, PB 35, 40014, Jyväskylä, Finland
- Moscow State University, Institute of Nuclear Physics, Leninskie gory, GSP-1, Moscow 119991, Russia
| | - Terhi T. Hongisto
- NanoScience Center, Department of Physics, University of Jyväskylä, PB 35, 40014, Jyväskylä, Finland
| | - Janne S. Lehtinen
- NanoScience Center, Department of Physics, University of Jyväskylä, PB 35, 40014, Jyväskylä, Finland
| | - Leena I. Leino
- NanoScience Center, Department of Physics, University of Jyväskylä, PB 35, 40014, Jyväskylä, Finland
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